Slender Body Theory for an Oscillating Ship 



For ^-^, > o; 



,(2) 



r c. 



$ic J C,(T) e 







'wJ'-'^'^ 



dr 



VCcT- 27)'' - 4c2t2 



;i^f L, 



(T) e 



^^(^-^^^^ 



dr 



y(^r+2y)'*- 4'£'t2 



fv 



iid I D,(T) e 

 1 



'w.^'-'^^- 



At 



\/(dT-27)^ - 4d2T2 



with 



(^L - /3oP^)^ - (47^ - Dp' , m2 = -47P(^L " /^qP^) ^gn (^-^i) 



-ySpP sgn (^-^1) - 27i - 



i(— T + 27) , 



+ 27 , C4 = i -^ r - 27 , D4 = i 2 -^ - 27 , 



c = 1 + 27 - VI + 47 , d = 1 + 27 + Vl + 47 • 



For 7 < 1/4: 



h = 1 - 27 - \/l -47 , 



-t = 1 - 2y + VI -47 



and 



For 7 > 1/4: 



and 



( 3) 



g: = 



h = -& = 27 



(3) i/3 



G„ = -4e 



i Ui-^l 



N„(T)e 

 -^0 



{/S(St+ 1)( 1-t) +i8T sgn(f-f j)} 



dr 



V(St+ 2)(St+ 1)(1-t)t 



179 



